Question

What is the volume of a sphere with a great circle that has an area of 224 pi centimeter squared?

Answer 1

The volume of the sphere is 14,043
`cm^(3)`

Explanation:

Firstly, in order to answer this question, we need to understand what is meant by the term great circle.

A great circle can be defined as a circle which has the same radius as that of the sphere from which it was formed. This can be pictured using an orange. An orange is a spherical shape and we can cut several circles across the length of the orange. However, not all these circles cut will have same diameter equal to that of the orange. The ones having the same diameter are referred to as great circles.

Since we have established that the sphere and the circle has the same radius/diameter, we can estimate the radius of the sphere from the area of the great circle.

Like all other circles, the great circle has an area which is A = π ×
`r^(2)`

224 π = π ×
`r^(2)`

⇒ 224 =
`r^(2)`

r =
`√(224)` cm

We can then proceed to calculate the volume of the sphere.

Mathematically, the volume V of a sphere can be calculated by;

V =
`(4)/(3)` × π ×
`r^(3)` = 4/3 × π ×
`(√(224))^(3)` = 4/3 × π × 224 × √224 = 14,043
`cm^(3)`